Examination of the proportional Hazard assumption in Cox regression model

The term survival analysis stands for the analysis of data where we have recorded the time period from a defined time origin up to a certain event for a number of individuals. The event is often called a "failure" and the length of time is called the "failure time". The difference between individuals' survival periods can be analysed using the nonparametric Kaplan-Meier method, semi parametric life table method and parametric methods. In addition, the most common approach to model covariate effects on survival is the Cox regression (proportional hazards) model where it is necessary that the proportional hazards assumption holds Cox regression model. The methods used in survival analysis are now applied in many fields, such as biology, engineering, medicine, quality control and credit risk modeling in finance. However, the application of survival analysis in the field of transport in Turkey has not been studied much. We studied a real data taken from İzmir ESHOT (Electricity, Water, Water Gas, Bus and Trolleybus) headquarters consisting of drivers accidents that happened between 2012-2014 years. The outcome variable is the survival time that is the time passed until the first accident happens. The explanatory variables are the district, the traffic jam, the bus capacity, the passenger number, the station number, the bus type, the driver age and the driver experience. We examined the proportional hazards assumption with "log(-log) plots", "Schoenfeld residual plots", "expected vs observed plots", "Arjas plots" and "using time dependent explanatory variables methods".